1. Field of the Invention
The present invention relates to a simulation model for the design of a semiconductor device which is used to estimate thermal drain noise from the DC characteristics of a MOSFET, a thermal drain noise analysis method using the model, and a simulation method and apparatus which simulate the electrical characteristics or circuit operation of a semiconductor device on a computer by means of the model.
2. Description of the Related Art
With the recent advances in high integration techniques for semiconductor devices such as ICs and LSIs, the generation of noise has become a serious problem as MOSFETs have been reduced in size. FIG. 1 shows the relationship between a frequency f and a drain current noise spectrum density Sid in MOSFETs manufactured by a 100-nm microfabrication technique. As shown in FIG. 1, 1/f noise (noise exhibiting a spectrum distribution almost inversely proportional to a frequency; also called flicker noise) is observed in a low-frequency region, whereas thermal noise (electrical noise caused by thermal agitation of electrons) is observed in a GHz band of high frequencies. 1/f noise and thermal noise are caused by physically different mechanisms. Of such noise, 1/f noise is relatively large and hence can be measured by a conventional DC test technique. Thermal noise is, however, small and hence is difficult to directly measure. For this reason, as the application of MOSFETs to radio-frequency (RF) circuits such as cellphones and wireless LANs has progressed, greater importance has been attached to countermeasures against thermal noise (see, for example, D. K. Shaeffer and T. H. Lee, “A 1.5 V 1.5 GHz CMOS low noise amplifier”, IEEE J. Solid-State Circuits, vol. 32, pp. 745–759, 1997).
FIG. 2 shows an increase in thermal noise with a decrease in the size of MOSFETs, and more specifically, the drain current noise spectrum density Sid [A2/Hz] as a function of the frequency f [GHz] in the case of gate length Lg=0.18 μm, 0.27 μm, 0.42 μm, 0.94 μm, and 0.97 μm. As the gate length Lg decreases, thermal noise increases. It is expected that when the gate length becomes smaller than 0.18 μm, thermal noise will increase more.
Noise generated in a circuit is one parameter that causes a deterioration in circuit characteristics. In designing a circuit, therefore, it is necessary to accurately predict noise by circuit simulation.
Conventionally, such noise is calculated as γ=⅔ by using the relational expression Sid=4 kTgds0γ for the drain current noise spectrum density Sid which is obtained from the Nyquist theorem equation (see H. Nyquist, Phys. Rev., 32, 110, 1928, “Thermal Agitation of Electric Charge in Conductors”).
That is, thermal noise is caused by heat, and the noise spectrum density per unit frequency is constant without exhibiting frequency dependence. This thermal noise has been theoretically explained by Nyquist, and its general expression is:SV=4kTR[V2/Hz]SI=4kTG[A2/Hz]  (1)where SV is the voltage noise spectrum density, SI is the current noise spectrum density, k is the Boltzmann constant, T is the absolute temperature, R is the resistance, and G is the conductance.
Consider the case of a MOSFET. First of all, according to expressions (1), letting Sid be the drain current noise spectrum density, a general expression can be written as follows:Sid=4kTgds  (2)In the case of a MOSFET, however, since a channel conductance gds depends on a bias voltage, gds is fixed to the value obtained when Vds=0, the drain current noise spectrum density is written asSid=4kTgds0γ  (3)and γ (thermal drain noise coefficient) is used to evaluate the characteristics of thermal noise.
Since gds is equal to gds0 when drain-source voltage Vds=0, γ is given as γ=1 by comparing equations (2) and (3). As Vds increases, gds decreases, and hence γ decreases. In the case of a long channel, it has been found experimentally and theoretically that 2/3< γ<1 in a linear region, and γ converges to γ=⅔ in a saturation region.
In the case of a short channel, it was found from actual measurements in R. P. Jindal, IEEE Trans. Elec. Dev. 1986, “Hot-Electron Effects on Channel Thermal Noise in Fine-Line NMOS Field-Effect Transistors” that γ increases to 1 or more. Although the cause for an increase in γ has not been theoretically explained, it is thought, according to G. Knoblinger, P. Klein, M. Tiebout, IEEE J. Solid-State Circuits, 2001, “A New Model for Thermal Channel Noise of Deep Submicron MOSFET's and its Application in RF-CMOS Design”, that the hot carrier effect is the cause.
As described above, since the value of thermal drain noise coefficient γ actually takes a value ranging from ⅔ to 1, circuit simulation cannot be accurately performed by calculation with γ=⅔.
According to one technique for solving this problem, thermal noise is measured under different bias conditions as in the case of a DC model, and γ is handled as a parameter. As described above, however, thermal noise is small and difficult to measure, and it takes much time to measure it. In addition, since an apparatus for such measurement is not generally used as compared with that for DC measurement, it is difficult to obtain a parameter on the basis of the measurement result on thermal noise.
Under the circumstances, demand has arisen for the development of a MOSFET model which allows high-precision estimation of thermal noise without direct measurement, a thermal noise analysis method, and a simulation method and apparatus which can accurately simulate the electrical characteristics or circuit operation of a semiconductor device on a computer by using a MOSFET model.
As described above, according to the conventional simulation model for the design of a semiconductor device, since calculation is performed with a fixed thermal drain noise coefficient, circuit simulation cannot be done with high precision. In order to solve this problem, thermal noise may be measured under different bias conditions, and a thermal drain noise coefficient may be handled as a parameter. It is, however, difficult to measure thermal noise, and it takes much time to measure it. It is therefore difficult to obtain a parameter on the basis of the measurement result.
Even if thermal drain noise is measured, it cannot be evaluated or analyzed.
In addition, the conventional semiconductor device simulation method and apparatus using this model cannot accurately simulate the electrical characteristics or circuit operation of a semiconductor device formed from microfabricated MOSFETs.